This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

This study relates to synthesis of bentonite-supported iron/copper nanoparticles through the biosynthesis method using eucalyptus plant leaf extract, which were then named E-Fe/Cu@B-NPs. The synthesised E-Fe/Cu@B-NPs were examined by a set of experiments involving a heterogeneous Fenton-like process that removed direct blue 15 (DB15) dye from wastewater. The resultant E-Fe/Cu@B-NPs were characterised by scanning electron microscopy, Brunauer–Emmet–Teller analysis, zeta potential analysis, Fourier transform infrared spectroscopy and atomic force microscopy. The operating parameters in batch experiments were optimised using Box–Behnken design. These parameters were pH, hydrogen peroxide (H₂O₂

Background: This clinical trial aims to evaluate the color changes of direct resin composite veneer (DCV) restorations based on spectrophotometric analysis of 4 different types of resin composites between the baseline immediately after polishing and after one year of follow-up. Materials and methods: 28 patients were assessed for eligibility for participation, aged between 18 and 38 years old, who indicated for DCV restorations in anterior maxillary teeth were considered for participation in this study. In total, 25 patients who met the inclusion criteria were selected (6 males and 19 females, mean age: 20.9 at the time of restoration placement), and 3 patients were excluded. Partic

    The main goal of the current research is to know -Environmental problems included in the content of the two science books (chemistry units) for intermediate stage

A list of environmental problems had been prepared  and  consisting of (8) main areas which are (air and atmosphere pollution, water pollution, soil pollution, energy, disturbance of biodiversity and environmental balance, waste management, food and medicinal pollution, investment of mineral wealth). Of which (60) sub-problems,  at that time the researcher analyzed the two science books (two chemistry units) for the intermediate stage of the academic year (2020-2021) in light of the list that was prepared, and the validity and consisten

Study of Direct Marketing techniques and determining the scope of the suitability of each of them in the application in the Iraqi market - An analytical and explorative study for sample of views for wholesaler in Baghdad. The essential idea of the research is to go into the most important concepts which have been mentioned in the direct marketing and determining its current and most important techniques and knowing the scope of applying these techniques in Baghdad main markets (Karrada, Jamilah, shorja, Baya area, zeyouna and new Baghdad) and which of those techniques most applicable in these markets. The research took a sample of (100) wholesalers who practice the activities of selling nutritional items, auto and outs spare part

  With occurrence of any financial crises, regardless at global or regional levels such as the great economic crises during 1929 – 1933 and the Asian financial crises at the end of twentieth century as well as the current global financial crises that started during second half 2008, we acknowledge that there are some critics loudly articulated accusing accountants and auditors for disparences, and they are numerical partner of financial manipulation as well as corrupted administrators with the company's administrators that they are difficulty. At this point, many suggestions and recommendation for upgrading the accounting system has been made.              &nbsp